Farm-yield Management When Production Rate is Yield Dependent
Abstract
In agricultural industries, unfavorable weather conditions, high infestation of pests and diseases lead to not only a lower farm-yield available for processing, but also a lower production rate in processing due to the inferior quality of the crop, a feature that is largely ignored by the academic literature. This paper studies the role of the yield-dependent production rate influencing the insights coming from traditional models that (often implicitly) assume yield-invariant production rate. We consider a firm that reserves farm space for an agricultural input under the yield and the open market price uncertainties; and, after these uncertainties are realized, processes the yield from the farm space and the input sourced from the open market to sell through different sales contracts. The production rate from each input is yield dependent and non-decreasing in the realized yield. We show that, contrary to common intuition, the firm may benefit from increasing yield variability, specifically, when the probability of achieving a higher production rate is moderate. Furthermore, a lower farm space dependency always better responds to the increasing yield variability, whereas this response crucially depends on the size of the reserved farm space when the production rate is yield invariant. We find that the cost of ignoring the yield-dependent nature of the production rate in procurement planning can be substantial, and this cost is very sensitive to the sales contract used. Our results have important implications about the procurement strategy and the sales contract choice of processors in agricultural industries.